How to Find Area Under Polar Curves (Calculus 2 Lesson 49)
In this video we learn how to calculate area under polar curves using a definite integral. We discuss how finding this area involves adding up the area of an infinite number of sectors between two angles and how it leads to the formula for calculating area under a polar curve. We go through a couple examples of calculating area under polar curves with each step explained along the way.
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This video series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Review of Area Under of a Curve (Rectangular)
2:06 Area Under a Polar Curve?
8:30 Formula for Area Under a Polar Curve
9:09 Example: Area Enclosed by r=6sinθ
21:19 Example: Area Enclosed by r=1+cosθ
31:45 Example: Area of One Petal of r=3cos(3θ)
46:24 Outro
📝 Examples Video: • Area Under Polar Curve...
⏩ Next Lesson: • Area Between Two Polar...
📺 Calculus 2 Playlist: • Calculus 2
📺 Calculus 1 Playlist: • Calculus 1
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